Question:
Katherine can finish a work in 88 days. Debra can finish the same work in 93 days while Rachel can finish the work in 98 days. How long will it take to finish it if they work together?
Correct Answer
30 12186/12961 days or 30.94 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Katherine = 88 days
And, the number of days required to finish the same work by Debra = 93 days
And, the number of days required to finish the same work by Rachel = 98 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 88 days the work is done by Katherine = 1
∴ The work done by Katherine in 1 day = 1/88
Similarly,
∵ In 93 days the work is done by Debra = 1
∴ The work done by Debra in 1 day = 1/93
Similarly,
∵ In 98 days the work is done by Rachel = 1
∴ The work done by Rachel in 1 day = 1/98 part
Now, the work done by Katherine, Debra, and Rachel together in 1 day
= Katherine's 1 day work + Debra's 1 day work + Rachel's 1 day work
= 1/88 + 1/93 + 1/98
= 4557 + 4312 + 4092/401016
= 12961/401016 part of work
This means in 1 day, 12961/401016 part of work is done by Katherine, Debra and Rachel working together.
Now, the number of days required to finish 12961/401016 part of work by Katherine, Debra, and Rachel working together = 1
∴ the number of days required to finish the whole work (1 work) by Katherine + Debra + Rachel together
= 1/12961/401016
= 1 × 401016/12961 = 401016/12961 days
= 30 12186/12961 days = or 30.94 days
Thus, Katherine, Debra, and Rachel working together will finish the total work (1 work) in 30 12186/12961 days = or 30.94 days Answer
Shortcut Trick to solve the problems based on time and work using formula
Case: If A can finish a work in a days, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= a × b × c/ab + ac + bc days.
Here given,
The number of days required to finish the work by Katherine = 88 days
And the number of days required to finish the same work by Debra = 93 days
And the number of days required to finish the work by Rachel = 98 days
Thus, the number of days required to finish the work by Katherine, Debra, and Rachel together = ?
Here a = 88 days
And, b = 93 days
And, c = 98 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Katherine, Debra, and Rachel working together
= 88 × 93 × 98/88 × 93 + 88 × 98 + 93 × 98 days
= 802032/8184 + 8624 + 9114 days
= 802032/25922 days
= 802032/25922 days
= 802032 ÷ 2/25922 ÷ 2 = 401016/12961 days
= 30 12186/12961 days or 30.94
Thus, Katherine, Debra, and Rachel together will finish the work in 30 12186/12961 days or 30.94 days Answer
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